Fit Two-Sample Underreported Count Models via JAGS

Fits Poisson, zero-inflated Poisson (ZIP), and negative binomial (NB) models for two independent underreported count samples using JAGS. Model selection is performed using the Deviance Information Criterion (DIC), Watanabe-Akaike Information Criterion (WAIC), and Pareto-smoothed importance sampling leave-one-out cross-validation (PSIS-LOO). For each criterion, the function applies a parsimony rule that favors the underreported Poisson model when its criterion value is within a specified threshold of the minimum value across the candidate models; otherwise, the model with the minimum criterion value is selected.

urc_two_mcmc(
  x,
  thresh = 2,
  prior_lambda1 = "dgamma(0.1,0.1)",
  prior_lambda2 = "dgamma(0.1,0.1)",
  prior_p1 = "dbeta(1,1)",
  prior_p2 = "dbeta(1,1)",
  prior_pi1 = "dbeta(1,1)",
  prior_pi2 = "dbeta(1,1)",
  prior_c1 = "dgamma(0.1,0.1)",
  prior_c2 = "dgamma(0.1,0.1)",
  n_iter = 8000,
  n_chains = 2,
  n_burnin = 4000,
  inits = NULL,
  seed = 123,
  parallel = FALSE
)

Arguments

x

A named list containing the data for JAGS models. Must include: yobs1, yobs2 (observed counts subject to underreporting), ystar1, ystar2 (true counts for validation), yval1, yval2 (validation observed counts)

thresh

Numeric. The threshold used for the parsimony rule. If the underreported Poisson model is within thresh units of the minimum value of a model-selection criterion, the Poisson model is selected as the preferred model; otherwise, the model with the minimum value of the criterion is selected. Applied separately to DIC, WAIC, and PSIS-LOO. Default is 2.

prior_lambda1

Prior for lambda (sample 1, Poisson/NB)

prior_lambda2

Prior for lambda (sample 2, Poisson/NB)

prior_p1

Prior for reporting probability (sample 1)

prior_p2

Prior for reporting probability (sample 2)

prior_pi1

Prior for zero-inflation probability (sample 1, ZIP only)

prior_pi2

Prior for zero-inflation probability (sample 2, ZIP only)

prior_c1

Prior for NB dispersion (sample 1, NB only)

prior_c2

Prior for NB dispersion (sample 2, NB only)

n_iter

Total number of MCMC iterations per chain.

n_chains

Number of MCMC chains.

n_burnin

Number of burn-in iterations.

inits

Optional initial values (function or list).

seed

Random seed for reproducibility.

parallel

Logical. If TRUE, model fitting is performed in parallel using the future and furrr frameworks. This enables simultaneous fitting of the Poisson, zero-inflated Poisson, and negative binomial models across multiple workers. If FALSE, the models are fitted sequentially.

Value

A named list containing:

models

A named list of fitted rjags model objects.

dics

A data frame containing the DIC value for each fitted model.

waics

A data frame containing the WAIC value for each fitted model.

loos

A data frame containing the PSIS-LOO value for each fitted model.

dic_best

The preferred model selected using the DIC-based parsimony rule.

waic_best

The preferred model selected using the WAIC-based parsimony rule.

loo_best

The preferred model selected using the PSIS-LOO-based parsimony rule.